The Virtual Element Method with curved edges

2017/11/12 by da Veiga, L. Beirão, Russo, A., Vacca, G. · 3 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1711.04306

Abstract

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy k ≥ 2, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence.

Cited by

• Benchmarking stabilized and self-stabilized p-virtual element methods with variable coefficients
• Effective numerical integration on complex shaped elements by discrete signed measures
• A Virtual Element Method on polyhedra with curved faces

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